χ_R(∣qubit_H⟩^⊗5) ≥ 4

H-type orbit, qubit.

Participate

Run it yourself, or point a coding agent at it.

git clone https://github.com/unitaryfoundation/stabrank
cd stabrank
# describe your decomposition in bounds/mybound.json
make fit BOUND=bounds/mybound.json ARGS=--write
make verify BOUND=bounds/mybound.json

fit solves for the exact coefficients, or tells you no exact combination of your terms reproduces the target. verify rebuilds the identity in exact arithmetic. If it passes, open a pull request adding the file and the leaderboard picks it up on the next build.

A bound the pipeline cannot check is recorded as cited and never takes a record.

← back to the board

Verification

reproduced certificate script asserted: CERTIFIED chi(qubit_H^5) >= 4

Compute

1 run; 0.02 CPU-hours; 0.01 h wall-clock; on Apple silicon laptop; the m=4 rank-3 exclusion re-runs inside the certificate.

Notes

Projection monotonicity from the m=4 rank-3 exclusion, re-run inside the certificate: χ(ψ ⊗ φ) ≥ χ(ψ) when φ has a nonzero computational amplitude. Puts the cell at 4 ≤ χ ≤ 6; the m=6 file cites the same certificate one copy further, and the m=5 upper file's note had asserted this bound without a file behind it.

Attribution

this repository · stabrank rank_exclusion.py · projection monotonicity applied to an exhaustive exclusion at lower m

Submission

JSON

{
  "schema_version": "0.1",
  "orbit": "qubit_H",
  "m": 5,
  "direction": "lower",
  "rank": 4,
  "provenance": {
    "author": "this repository",
    "reference": "stabrank rank_exclusion.py",
    "method": "projection monotonicity applied to an exhaustive exclusion at lower m",
    "date": "2026-09-18",
    "github": [
      "vprusso"
    ],
    "compute": {
      "cpu_hours": 0.02,
      "wall_clock_hours": 0.01,
      "runs": 1,
      "hardware": "Apple silicon laptop; the m=4 rank-3 exclusion re-runs inside the certificate"
    }
  },
  "notes": "Projection monotonicity from the m=4 rank-3 exclusion, re-run inside the certificate: chi(psi (x) phi) >= chi(psi) when phi has a nonzero computational amplitude. Puts the cell at 4 <= chi <= 6; the m=6 file cites the same certificate one copy further, and the m=5 upper file's note had asserted this bound without a file behind it.",
  "certificate": {
    "script": "verify_challenge/cert_qubit_h_m6_from_m4.py",
    "expect": "CERTIFIED chi(qubit_H^5) >= 4"
  }
}